Zadanie 3
[tex]S=\frac{a}{1-q} \ \ \ \ \ \ \ \ \ \ |\cdot (1-q) \\ \\ S(1-q)=a \\ \\ S-Sq=a \\ \\ -Sq=a-S \ \ \ \ \ \ \ \ \ \ |:(-S) \\ \\ q=\frac{a-S}{-S} \\ \\ \mathbf{q=-\frac{a}{S}+1}[/tex]
Oczywiście przy założeniu, że [tex]q\neq 1[/tex] i [tex]S\neq 0[/tex].
Zadanie 5
[tex]\frac{3x-6}{x-1} +\frac{6x-1}{2x+2}=\frac{3(x-2)}{x-1} +\frac{6x-1}{2(x+1)}=\frac{6(x-2)(x+1)}{2(x-1)(x+1)} +\frac{(6x-1)(x-1)}{2(x+1)(x-1)}= \\ \\ =\frac{6(x^2+x-2x-2)}{2(x-1)(x+1)} +\frac{6x^2-6x-x+1}{2(x+1)(x-1)}=\frac{6x^2-6x-12}{2(x-1)(x+1)} +\frac{6x^2-7x+1}{2(x+1)(x-1)}= \\ \\ =\frac{6x^2-6x-12+6x^2-7x+1}{2(x^2-1)}= \frac{12x^2-13x-11}{2x^2-2}[/tex]
Przy założeniu, że [tex]x\neq -1[/tex] i [tex]x\neq 1[/tex].
